We present the results of Near-Infrared Camera and Multi-Object Spectrometer (NICMOS) imaging of a sample of 19 high-mass passively evolving galaxies with 1.2 < z < 2, taken primarily from the Gemini Deep Deep Survey (GDDS). Around 80% of galaxies in our GDDS sample have spectra dominated by stars with ages gsim1 Gyr. Our rest-frame R-band images show that most of these objects have compact regular morphologies which follow the classical R 1/4 law. These galaxies scatter along a tight sequence in the size versus surface brightness parameter space which defines the Kormendy relation. Around one-third (3/10) of the massive red objects in the GDDS sample are extraordinarily compact, with effective radii under 1 kpc. Our NICMOS observations allow the detection of such systems more robustly than is possible with optical (rest-frame UV) data, and while similar systems have been seen at z gsim 2, this is the first time such systems have been detected in a rest-frame optical survey at 1.2 < z < 2. We refer to these compact galaxies as "red nuggets," and note that similarly compact massive galaxies are completely absent in the nearby universe. We introduce a new "stellar mass Kormendy relation" (stellar mass density versus size) which we use to single out the effects of size evolution from those of luminosity and color evolution in stellar populations. The 1 < z < 2 passive galaxies have mass densities that are an order of magnitude larger then early-type galaxies today and are comparable to the compact distant red galaxies at 2 < z < 3. We briefly consider mechanisms for size evolution in contemporary models focusing on equal-mass mergers and adiabatic expansion driven by stellar mass loss. Neither of these mechanisms appears to be able to transform the high-redshift Kormendy relation into its local counterpart, leaving the origin and fate of these compact "red nuggets" unresolved.